Line-depth ratios as indicators of effective temperature and surface gravity

The analysis of stellar spectra depends on the effective temperature (T_eff) and the surface gravity (log g). However, the estimation of log g with high accuracy is challenging. A classical approach is to search for log g that satisfies the ionization balance, i.e. the abundances from neutral and ionized metallic lines being in agreement. We propose a method of using empirical relations between T_eff, log g, and line-depth ratios, for which we meticulously select pairs of Fe I and Fe II lines and pairs of Ca I and Ca II lines. Based on YJ-band (0.97-1.32 $\mu$m) high-resolution spectra of 42 FGK stars (dwarfs to supergiants), we selected 5 Fe I-Fe II and 4 Ca I-Ca II line pairs together with 13 Fe I-Fe I pairs (for estimating T_eff), and derived the empirical relations. Using such relations does not require complex numerical models and tools for estimating chemical abundances. The relations we present allow one to derive T_eff and log g with a precision of around 50 K and 0.2 dex, respectively, but the achievable accuracy depends on the accuracy of the calibrators' stellar parameters. It is essential to revise the calibration by observing stars with accurate stellar parameters available, e.g. stars with asteroseismic log g and stars analysed with complete stellar models taking into account the effects of non-local thermodynamic equilibrium and convection. In addition, the calibrators we used have a limited metallicity range, -0.2 < [Fe/H] < +0.2 dex, and our relations need to be tested and re-calibrated based on a calibrating data set for a wider range of metallicities.